An Effective Strategy to Maintain the CALPHAD Atomic Mobility Database of Multicomponent Systems and Its Application to Hcp Mg–Al–Zn–Sn Alloys

In this paper, a general and effective strategy was first developed to maintain the CALPHAD atomic mobility database of multicomponent systems, based on the pragmatic numerical method and freely accessible HitDIC software, and then applied to update the atomic mobility descriptions of the hcp Mg–Al–Zn, Mg–Al–Sn, and Mg–Al–Zn–Sn systems. A set of the self-consistent atomic mobility database of the hcp Mg–Al–Zn–Sn system was established following the new strategy presented. A comprehensive comparison between the model-predicted composition–distance profiles/inter-diffusivities in the hcp Mg–Al–Zn, Mg–Al–Sn, and Mg–Al–Zn–Sn systems from the presently updated atomic mobilities and those from the previous ones that used the traditional method indicated that significant improvement can be achieved utilizing the new strategy, especially in the cases with sufficient experimental composition–distance profiles and/or in higher-order systems. Furthermore, it is anticipated that the proposed strategy can serve as a standard for maintaining the CALPHAD atomic mobility database in different multicomponent systems.


Introduction
As is well known, the mechanical properties of metallic materials, such as strength, ductility, and hardness, are closely related to their microstructural formation during various preparation processes such as solidification, solid solution, and aging [1,2]. To achieve a comprehensive understanding of different preparation processes, accurate diffusion coefficients of composition and temperature dependence should be the prerequisite. For typical multicomponent technical alloys, direct experimental measurement of the complex diffusion coefficient matrices seems to be very difficult [3]. One alternative substitution in the CALPHAD (CALculation of PHAse Diagram) community is to predict a variety of composition-and temperature-dependent diffusion coefficients from the established atomic mobility database of the target alloys together with the corresponding thermodynamic database [4].
In terms of the CALPHAD framework, the traditional procedure for establishing the atomic mobility database of multicomponent alloys is referred to Figure 6.3 of a recent book chapter by Zhang and Chen [5], and it is also briefly described as follows: (i) Step 1: conduct a literature review of various diffusion properties in boundary unary, binary, ternary, and higher-order systems including the diffusion coefficients such as self/impurity diffusion coefficients for unary systems, interdiffusion coefficients for binary and ternary systems, and tracer coefficients for binary and higher-order systems as well as the experimental composition-distance profiles for quaternary and higher-order systems; (ii) Step 2: supplement the diffusion coefficients in boundary unary, binary, and ternary systems lacking the diffusion coefficients. The self/impurity diffusion coefficients of unary systems and tracer diffusion coefficients for binary and higher-order systems can be determined by 1.
The original atomic mobility descriptions of the target multicomponent system, together with the thermodynamic descriptions, should be ready or re-constructed according to the corresponding publication(s).

2.
A critical review of all the composition-distance profiles of diffusion multiples/couples in ternary and higher-order systems available in the literature should be conducted both before and after the publication/release of the original atomic mobility database. 3.
The atomic mobility descriptions in each boundary ternary system should be updated by means of the HitDIC software based on the reviewed composition-distance profiles.
It should be noted that the atomic mobility descriptions in all the boundary binaries are fixed during the entire stage. Moreover, the reliability of the updated atomic mobilities should be validated by the experimental composition-distance profiles as well as the evaluated interdiffusion coefficients available in the literature.

4.
Based on the updated atomic mobilities of boundary ternary systems, all the composition-distance profiles in the higher-order systems should be input into the HitDIC software to assess the possible interaction parameters in high-order systems. The interaction parameters in higher-order systems are introduced if their addition can really improve the fit to most of the experimental composition profiles. During this step, it should be noted that the interaction parameters of ternary atomic mobilities can be updated if a better fit to the experimental composition profiles in higher-order system can be achieved. 5.
One needs to validate the updated atomic mobility database by comprehensively comparing the predicted diffusion properties with the experimental ones in all the related ternary, quaternary, and higher-order systems, verify the updated atomic mobility database by applying real applications if available, and finalize the documentation. Here, the "c-x" represents the "composition-distance".

Literature Review on Diffusion Information in Hcp Mg-Al-Zn-Sn Alloys
In this paper, the atomic mobilities of three boundary binaries (i.e., hcp Mg-Al, Mg Zn, and Mg-Sn) were directly taken from Zhong et al. [32] and fixed during th subsequent assessment of atomic mobilities in higher-order systems (i.e., hcp Mg-Al-Zn Mg-Al-Sn, and Mg-Al-Zn-Sn); thus, there was no need to conduct the literature review for those boundary binaries. In the following, all the measured composition-distanc profiles in the hcp Mg-Al-Zn, Mg-Al-Sn, and Mg-Al-Zn-Sn systems available in th literature are briefly introduced and are also summarized in Table 1. Moreover, in orde to validate the reliability of the subsequently assessed mobilities, the experimental report on different diffusivities in the hcp Mg-Al-Zn, Mg-Al-Sn, and Mg-Al-Zn-Sn system were also briefly described as follows.
For the hcp Mg-Al-Zn ternary system, the interdiffusion behaviors in seven group of diffusion couples at 673 and 723 K were investigated by Kammerer et al. [35]. Thereinto the composition-distance profiles of four groups (i.e., Mg-9.08Al/Mg-2.55Zn, Mg 0.87Al/Mg-1.12Zn, Mg-9.10Al/Mg-2.03Zn, and Mg-2.27Al/Mg-1.06Zn, in at.%) wer reported, while only the diffusion paths were given for the other three groups (i.e., Mg 3Al/Mg-1Zn, Mg-3Al/Mg-0.5Zn, and Mg/Mg-3Al-0.5Zn, in at.%). However, it should b noted that the composition-distance profiles of Mg-0.87Al/Mg-1.12Zn from Kammerer e al. [35] were not reasonable based on the analysis of Wang et al. [36]. In addition, th composition-distance profiles in the AZ91 (Mg-9Al-1Zn, in wt.%)/Mg diffusion couple a 663 and 708 K were also determined by Bryan et al. [33]. But Zhong et al. [32] pointed ou that the existence of MgO on the surface of the diffusion couples showed a noticeabl effect on the interdiffusion between pure Mg and AZ91 in the work of Bryan et al. [33 Hence, the composition-distance profiles of three groups (i.e., Mg-9.08Al/Mg-2.55Zn, Mg 9.10Al/Mg-2.03Zn, and Mg-2.27Al/Mg-1.06Zn, in at.%) from Kammerer et al. [35] wer employed in the present optimization, while the composition-distance profiles from Bryan et al. [33] as well as the composition-distance profiles of Mg-0.87Al/Mg-1.12Zn an diffusion paths from Kammerer et al. [35] were not.
For the hcp Mg-Al-Sn ternary system, Zhou et al. [37] determined the composition distance profiles at 673 and 723 K based on the diffusion couple technique. Moreover, th composition-distance profiles for the Mg-Al-Sn ternary diffusion couples at 723, 773, an 823 K were determined by Zhang et al. [34], respectively. The experimental data from bot Zhou et al. [37] and Zhang et al. [34] were employed in the present optimization.
As for the hcp Mg-Al-Zn-Sn quaternary system, the composition-distance profile in one quaternary diffusion couple annealed at 773 K for 250 h were measured by Brya et al. [33] and thus were considered during the present assessment of the atomi mobilities. Figure 1. An effective strategy for maintaining the atomic mobility database of multicomponent systems proposed in this work. Here, the "c-x" represents the "composition-distance".

Literature Review on Diffusion Information in Hcp Mg-Al-Zn-Sn Alloys
In this paper, the atomic mobilities of three boundary binaries (i.e., hcp Mg-Al, Mg-Zn, and Mg-Sn) were directly taken from Zhong et al. [32] and fixed during the subsequent assessment of atomic mobilities in higher-order systems (i.e., hcp Mg-Al-Zn, Mg-Al-Sn, and Mg-Al-Zn-Sn); thus, there was no need to conduct the literature review for those boundary binaries. In the following, all the measured composition-distance profiles in the hcp Mg-Al-Zn, Mg-Al-Sn, and Mg-Al-Zn-Sn systems available in the literature are briefly introduced and are also summarized in Table 1. Moreover, in order to validate the reliability of the subsequently assessed mobilities, the experimental reports on different diffusivities in the hcp Mg-Al-Zn, Mg-Al-Sn, and Mg-Al-Zn-Sn systems were also briefly described as follows.
For the hcp Mg-Al-Zn ternary system, the interdiffusion behaviors in seven groups of diffusion couples at 673 and 723 K were investigated by Kammerer et al. [35]. Thereinto, the composition-distance profiles of four groups (i.e., Mg-9.08Al/Mg-2.55Zn, Mg-0.87Al/Mg-1.12Zn, Mg-9.10Al/Mg-2.03Zn, and Mg-2.27Al/Mg-1.06Zn, in at.%) were reported, while only the diffusion paths were given for the other three groups (i.e., Mg-3Al/Mg-1Zn, Mg-3Al/Mg-0.5Zn, and Mg/Mg-3Al-0.5Zn, in at.%). However, it should be noted that the composition-distance profiles of Mg-0.87Al/Mg-1.12Zn from Kammerer et al. [35] were not reasonable based on the analysis of Wang et al. [36]. In addition, the compositiondistance profiles in the AZ91 (Mg-9Al-1Zn, in wt.%)/Mg diffusion couple at 663 and 708 K were also determined by Bryan et al. [33]. But Zhong et al. [32] pointed out that the existence of MgO on the surface of the diffusion couples showed a noticeable effect on the interdiffusion between pure Mg and AZ91 in the work of Bryan et al. [33]. Hence, the composition-distance profiles of three groups (i.e., Mg-9.08Al/Mg-2.55Zn, Mg-9.10Al/Mg-2.03Zn, and Mg-2.27Al/Mg-1.06Zn, in at.%) from Kammerer et al. [35] were employed in the present optimization, while the composition-distance profiles from Bryan et al. [33] as well as the composition-distance profiles of Mg-0.87Al/Mg-1.12Zn and diffusion paths from Kammerer et al. [35] were not.
For the hcp Mg-Al-Sn ternary system, Zhou et al. [37] determined the compositiondistance profiles at 673 and 723 K based on the diffusion couple technique. Moreover, the composition-distance profiles for the Mg-Al-Sn ternary diffusion couples at 723, 773, and 823 K were determined by Zhang et al. [34], respectively. The experimental data from both Zhou et al. [37] and Zhang et al. [34] were employed in the present optimization. Mg-Al-Zn-Sn quaternary system Mg-0.64Al-0.04Sn-0.59Zn/Mg-0.79Al-2.42Sn-0.66Zn 773 250 [33] , used in the optimization process; , only used for comparison.
As for the hcp Mg-Al-Zn-Sn quaternary system, the composition-distance profiles in one quaternary diffusion couple annealed at 773 K for 250 h were measured by Bryan et al. [33] and thus were considered during the present assessment of the atomic mobilities.
Besides the above experimental information on the composition-distance profiles, there are also some reports on the inter-diffusivities available in the literature. Based on the experimental composition profiles in the hcp Mg-Al-Zn system by Kammerer et al. [35], Wang et al. [36] [37] also using the W-G method. Moreover, the inter-diffusivities of the hcp Mg-Al-Sn system were also determined by Zhang et al. [34] by means of the M-K method. As indicated above, all the related interdiffusion coefficients in ternary systems were not used in the assessment procedure but employed to validate the finally obtained atomic mobilities.

Results and Discussion
The thermodynamic descriptions for the Mg-Al-Zn-Sn quaternary system from our previous publications [39][40][41] were directly employed in the present work for providing accurate thermodynamic properties. In the following, the atomic mobilities in the hcp Mg-Al-Zn and hcp Mg-Al-Sn ternary systems were first updated by fixing the atomic mobilities in boundary binaries, from which the atomic mobility database in the hcp Mg-Al-Zn-Sn quaternary system was then established.
In the hcp Mg-Al-Zn ternary system, the composition-distance profiles measured by Kammerer [35] (except for those in the Mg-0.87Al/Mg-1.12Zn diffusion couple, in at.%) together with the atomic mobility descriptions of boundary binaries as well as the thermodynamic descriptions were first provided as input in HitDIC software. Subsequently, the initial values of the interaction parameters (i.e., Φ Mg,Zn Al and Φ Mg,Al Zn ) of the ternary system were automatically set, and the optimization of the two parameters was carried out automatically by the HitDIC software until the best fit between the model-predicted composition-distance profiles and the experimental data was achieved. Finally, the established atomic mobility database of the hcp Mg-Al-Zn ternary system was validated by comparing the predicted diffusion properties with the corresponding experimental data. Moreover, a similar strategy was adopted for the hcp Mg-Al-Sn ternary system.
As for the hcp Mg-Al-Zn-Sn quaternary system, the experimental compositiondistance profiles by Bryan et al. [33] together with the updated atomic mobility descriptions of the hcp Mg-Al-Zn and Mg-Al-Sn as well as the thermodynamic descriptions of the hcp Mg-Al-Zn-Sn quaternary systems were first provided as the input in the HitDIC software. Subsequently, the assessment of the interaction parameters in the ternary and/or quaternary systems was automatically performed. It was found that introduction of an interaction parameter (i.e., Φ Mg,Sn Zn ) can result in the best fit to the experimental data. The finally obtained atomic mobility parameters of the hcp Mg-Al-Zn-Sn quaternary system are summarized in Table 2.

Hcp Mg-Al-Zn Ternary System
The model-predicted composition-distance profiles of four diffusion couples (i.e., Mg-9.08Al/Mg-2.55Zn at 673 K for 8 h, Mg/Mg-0.87Al-1.12Zn at 673 K for 24 h, Mg-9.10Al/Mg-2.03Zn at 723 K for 4 h, and Mg-2.77Al/Mg-1.06Zn at 723 K for 5 h, in at.%) according to the present atomic mobilities (solid lines) are displayed in Figure 2, compared with the corresponding experimental data (in symbols) by Kammerer et al. [35]. The model-predicted results by Zhong et al. [32] are also superimposed as dashed lines in the figure for direct comparison with the present results. Without specification, all the model-predicted results of Zhong et al. [32] are taken exactly from their original publication. As can be seen in Figure 2, the predicted results from the present work are consistent with those from Zhong et al. [32], and both predicted results are in good agreement with the experimental composition-distance profiles [35], expect for Figure 2b. As shown in Figure 2b, a large deviation between the model-predicted composition-distance profile of Zn and the experimental ones can be observed. This fact is quite normal because the composition-distance profiles of Mg/Mg-0.87Al-1.12Zn at 673 K for 24 h are not reasonable based on the suggestion by Wang et al. [36] and, thus, were not employed in the present optimization. Furthermore, the model-predicted diffusion paths at 673 and 723 K, based on the present atomic mobilities together with those by Zhong et al. [32], are shown in Figure 3 compared with the experimental data [35]. The diffusion paths predicted according to the present atomic mobilities are in very good agreement with the experimental data [35] and also the ones by Zhong et al. [32]. Moreover, the comparison between the model-predicted composition-distance profiles due to the present atomic mobilities and the experimental data by Bryan et al. [33] as well as those by Zhong et al. [32] are displayed in the Supplementary Materials for readers' reference. As can be seen Figur S1, certain deviations exist between the simulated composition profiles of Al/Zn and the experimental data. This is because MgO exits on the surface of the diffusion couples, as pointed out by Zhong et al. [32], and hinders the diffusion of both Al and Zn. Thus, the composition-distance profiles of Bryan et al. [33] were not considered in the present update of atomic mobilities. Table 2. List of the atomic mobility parameters of hcp the Mg-Al-Zn-Sn system assessed in the present work together with those taken in the literature [32].

Mobility Parameters References
Mobility of Mg According to the presently updated atomic mobility descriptions together with the thermodynamic descriptions [42], the interdiffusion coefficients of the hcp Mg-Al-Zn system over the composition range of 0-5.0 at.% Al and 0-3.0 at.% Zn at 623, 673, and 723 K are predicted in Figure 4. AlZn ) was adopted for the label of ordinate of Figure 4c in order to facilitate the analysis. The sign of cross-interdiffusion coefficients had been analyzed in detail by Liu et al. [43] in terms of thermodynamics. According to Liu et al. [43], the cross-interdiffusion coefficient D Mg AlZn in the hcp Mg-Al-Zn ternary system can be expressed as follows: where M Al , M Zn , and M Mg are the atomic mobilities for Al, Zn, and Mg, respectively.
x Al , x Zn , and x Mg are the mole fractions for Al, Zn, and Mg, respectively. µ Al and µ Mg represent the chemical potentials of Al and Mg, respectively. Because the term before (1) is positive, the negative sign of D Mg AlZn is determined by the ∂(µ Al − µ Mg )/∂x Zn . As can be seen in Figure 4c (1):

Hcp Mg-Al-Zn Ternary System
The model-predicted composition-distance profiles of four diffusion couples (i.e., Mg-9.08Al/Mg-2.55Zn at 673 K for 8 h, Mg/Mg-0.87Al-1.12Zn at 673 K for 24 h, Mg-9.10Al/Mg-2.03Zn at 723 K for 4 h, and Mg-2.77Al/Mg-1.06Zn at 723 K for 5 h, in at.%) according to the present atomic mobilities (solid lines) are displayed in Figure 2, compared with the corresponding experimental data (in symbols) by Kammerer et al. [35]. The model-predicted results by Zhong et al. [32] are also superimposed as dashed lines in the figure for direct comparison with the present results. Without specification, all the model-predicted results of Zhong et al. [32] are taken exactly from their original publication. As can be seen in Figure 2, the predicted results from the present work are consistent with those from Zhong et al. [32], and both predicted results are in good agreement with the experimental composition-distance profiles [35], expect for Figure 2b. As shown in Figure 2b, a large deviation between the model-predicted compositiondistance profile of Zn and the experimental ones can be observed. This fact is quite normal because the composition-distance profiles of Mg/Mg-0.87Al-1.12Zn at 673 K for 24 h are not reasonable based on the suggestion by Wang et al. [36] and, thus, were not employed in the present optimization. Furthermore, the model-predicted diffusion paths at 673 and 723 K, based on the present atomic mobilities together with those by Zhong et al. [32], are shown in Figure 3 compared with the experimental data [35]. The diffusion paths predicted according to the present atomic mobilities are in very good agreement with the experimental data [35] and also the ones by Zhong et al. [32]. Moreover, the comparison between the model-predicted composition-distance profiles due to the present atomic mobilities and the experimental data by Bryan et al. [33] as well as those by Zhong et al. [32] are displayed in the Supplementary Materials for readers' reference. As can be seen Figure S1, certain deviations exist between the simulated composition profiles of Al/Zn and the experimental data. This is because MgO exits on the surface of the diffusion couples, as pointed out by Zhong et al. [32], and hinders the diffusion of both Al and Zn. Thus, the composition-distance profiles of Bryan et al. [33] were not considered in the present update of atomic mobilities.   to the present atomic mobilities (solid lines), compared with those of Zhong et al. [32] (dashed lines) and the experimental data [35] (in symbols). According to the presently updated atomic mobility descriptions together with the thermodynamic descriptions [42], the interdiffusion coefficients of the hcp Mg-Al-Zn system over the composition range of 0-5.0 at.% Al and 0-3.0 at.% Zn at 623, 673, and 723 K are predicted in Figure 4.
where MAl, MZn, and MMg are the atomic mobilities for Al, Zn, and Mg, respectively. xAl, xZn, and xMg are the mole fractions for Al, Zn, and Mg, respectively. μAl and μMg represent the chemical potentials of Al and Mg, respectively. Because the term before ( ) (1) According to Equation (2)  To further illustrate the reliability of the presently updated atomic mobilities, the calculated main inter-diffusivities according to the present work are compared with the determined ones by Wang et al. [36] in Figure 5a. Along the diagonal lines, the modelpredicted values are exactly equal to the experimental ones. The region of empirical errors for inter-diffusivities is constructed by the two dashed lines that represent the interdiffusion coefficients multiplied with a pre-factor of 2 or 0.5, respectively, according To further illustrate the reliability of the presently updated atomic mobilities, the calculated main inter-diffusivities according to the present work are compared with the determined ones by Wang et al. [36] in Figure 5a. Along the diagonal lines, the modelpredicted values are exactly equal to the experimental ones. The region of empirical errors for inter-diffusivities is constructed by the two dashed lines that represent the interdiffusion coefficients multiplied with a pre-factor of 2 or 0.5, respectively, according to the suggestion in [44]. A similar plot was also made in Figure 5b between the calculated main interdiffusivities by Zhong et al. [32] and the ones determined by Wang et al. [36]. Based on the comparison in Figure 5a,b, it can be found that the calculated main interdiffusion coefficients from the present work are consistent with those of Zhong et al. [32], and the calculated main interdiffusion coefficients in both the present work and Zhong et al. [32] agree well with all the experimental data (within the dashed lines), expected for 6 values marked by black circles in the figure. It should be noted that those 6 points marked by black circles were determined by Wang et al. [36] based on three diffusion couples (i.e., Mg-3Al/Mg-1Zn, Mg-3Al/Mg-0.5Zn, and Mg-0.87Al/Mg-1.12Zn) from Kammerer et al. [35] of which the composition-distance profiles were not employed in the present optimization because the original experimental data were either unreasonable (i.e., Mg-0.87Al/Mg-1.12Zn) or not provided (i.e., Mg-3Al/Mg-1Zn and Mg-3Al/Mg-0.5Zn) according to the original publications. to the suggestion in [44]. A similar plot was also made in Figure 5b between the calculated main inter-diffusivities by Zhong et al. [32] and the ones determined by Wang et al. [36]. Based on the comparison in Figure 5a,b, it can be found that the calculated main interdiffusion coefficients from the present work are consistent with those of Zhong et al. [32], and the calculated main interdiffusion coefficients in both the present work and Zhong et al. [32] agree well with all the experimental data (within the dashed lines), expected for 6 values marked by black circles in the figure. It should be noted that those 6 points marked by black circles were determined by Wang et al. [36] based on three diffusion couples (i.e., Mg-3Al/Mg-1Zn, Mg-3Al/Mg-0.5Zn, and Mg-0.87Al/Mg-1.12Zn) from Kammerer et al. [35] of which the composition-distance profiles were not employed in the present optimization because the original experimental data were either unreasonable (i.e., Mg-0.87Al/Mg-1.12Zn) or not provided (i.e., Mg-3Al/Mg-1Zn and Mg-3Al/Mg-0.5Zn) according to the original publications. Based on the above analysis, the presently updated atomic mobilities of the hcp Mg-Al-Zn based on the newly proposed strategy are reliable and can give as good fit to all the experimental properties as of the recent publication [32] using the traditional approach.

Hcp Mg-Al-Sn Ternary System
Figures 6 and 7 display the model-predicted composition-distance profiles of eight diffusion couples (i.e., Mg-0.52Sn/Mg-7.81Al, Mg-1.00Sn/Mg-7.37Al, Mg-2.30Al-0.83Sn/Mg, and Mg-8.00Al-0.46Sn/Mg, annealed at 673 K for 216 h, in at.%; Mg-1.04Sn/Mg-3.59Al, Mg-1.07Sn/Mg-7.63Al, Mg/Mg-7.86Al-0.53Sn, and Mg-2.3Al-0.9Sn/Mg, annealed at 723 K for 216 h, in at.%) from the present work (solid lines) compared with the experimental data (in symbols) by Zhou et al. [37]. The model-predicted results according to Zhong et al. [32] (dashed lines) are also superimposed in the figure for direct comparison. Figures 8 and 9 also show the model-predicted composition-distance profiles of 10 diffusion couples (i.e., Mg/Mg-2.77Al-0.97Sn, Mg-1.46Sn/Mg-3.81Al, Mg-0.96Al-1.48Sn/Mg, and Mg-0.98Sn/Mg-1.92Al, annealed at 773 K for 6 h, in at.%; Mg-2.63Al-0.94Sn/Mg, Mg-1.43Sn/Mg-3.80Al, and Mg-1.89Al/Mg-0.97Sn, annealed at 723 K for 9 h, in at.%; Mg/Mg-1.43Al-0.92Sn, Mg-1.45Sn/Mg-3.74Al, and Mg-0.98Sn/Mg-1.83Al, annealed at 823 K for 3 h, in at.%) according to the present atomic mobilities and also those from Zhong et al. [32] compared with the experimental data by Zhang et al. [34]. As can be seen in Figures 6-9, the model-predicted composition-distance profiles according to the present work are in better agreement with the experimental data by Zhou et al. [37] and Zhang et al. [34] than the model-predicted ones due from Zhong et al. [32], especially in the figures, i.e., Figure 6a,b, Figure 7a,b, Figure 8b,d and Figure 9b,c,e,f. Furthermore, the model-predicted diffusion paths at 673, 723, 773, and 823 K, based on the presently updated atomic mobilities and also those by Zhong et al. [32], are displayed in Figure 10 compared with the experimental data from Zhou et al. [37] and Zhang et al. [34]. As can be seen in Figure 10, the model-predicted diffusion paths by the present work again agree better with the experimental data [34,37] than the model-predicted ones by Zhong et al. [32]. and Zhang et al. [34] than the model-predicted ones due from Zhong et al. [32], especially in the figures, i.e., Figures 6a,b, 7a,b, 8b,d and 9b,c,e,f. Furthermore, the model-predicted diffusion paths at 673, 723, 773, and 823 K, based on the presently updated atomic mobilities and also those by Zhong et al. [32], are displayed in Figure 10 compared with the experimental data from Zhou et al. [37] and Zhang et al. [34]. As can be seen in Figure  10, the model-predicted diffusion paths by the present work again agree better with the experimental data [34,37] than the model-predicted ones by Zhong et al. [32].  Based on the updated atomic mobility descriptions by the present work together with the thermodynamic descriptions [39], the inter-diffusivities of the hcp Mg-Al-Sn system over the composition range of 0-5.0 at.% Al and 0-2.0 at.% Sn at 723, 773, and 823 K are predicted in Figure 11. Similar to the hcp Mg-Al-Zn system, the interdiffusion coefficients of the hcp Mg-Al-Sn system were also processed with a logarithm. As shown in Figure 11a where M Al , M Sn , and M Mg are the atomic mobilities for Al, Sn, and Mg, respectively.
x Al , x Sn , and x Mg are the mole fractions for Al, Sn, and Mg, respectively. µ Al , µ Sn , and µ Mg represent the chemical potentials of Al, Sn, and Mg, respectively. Here, it should be noted that the signs of D

Mg
AlSn and D

Mg
SnAl are positive, which are determined by the terms ∂(µ Al − µ Mg )/∂x Sn and ∂(µ Sn − µ Mg )/∂x Al , respectively. As can be seen in Figure 11c (3) and (4). Figure 12a,b respectively show the calculated main interdiffusion coefficients according to the present atomic mobilities and those of Zhong et al. [32], compared with the experimental data [34,37]. Along the diagonal lines, the model-predicted values are exactly equal to the experimental ones. The two dashed lines represent the interdiffusion coefficients multiplied by a pre-factor of 2 or 0.5, respectively. A comparison between Figure 12a,b clearly indicates that the calculated interdiffusion coefficients from the present work can reproduce more experimental data than those by Zhong et al. [32].         Based on the updated atomic mobility descriptions by the present work together with the thermodynamic descriptions [39], the inter-diffusivities of the hcp Mg-Al-Sn system over the composition range of 0-5.0 at.% Al and 0-2.0 at.% Sn at 723, 773, and 823 K are predicted in Figure 11. Similar to the hcp Mg-Al-Zn system, the interdiffusion coefficients of the hcp Mg-Al-Sn system were also processed with a logarithm. As shown in Figure   Figure 10. Model-predicted diffusion paths in the hcp Mg-Al-Sn system at (a) 673 K for 216 h, (b) 723 K for 216 and 9 h, (c) 773 K for 6 h, and (d) 823 K for 3 h from the present mobilities (solid lines) compared with those of Zhong et al. [32] (dashed lines) and the experimental data [34,37] (in symbols).
Based on the above comprehensive comparison among the model-predicted results from the present work, the ones by Zhong et al. [32], and the experimental data [34,37], the reliability of the atomic mobility descriptions of the hcp Mg-Al-Sn system was significantly improved by using the newly proposed strategy compared with the traditional approach. The major reason lies in that although 18 groups of diffusion couples were investigated by Zhou et al. [37] and Zhang et al. [34], only very scattered experimental interdiffusion coefficients at the intersection compositions of diffusion paths can be determined by the traditional methods and then utilized in the traditional optimization process, which may lead to the lower accuracy of the obtained atomic mobility descriptions. By contrast, all 18 groups of composition-distance profiles can be employed in the optimization process using the new strategy based on HitDIC, which can largely improve the reliability of the atomic mobility descriptions. Figure 13 displays the comparison between the model-predicted composition-distance profiles of the only quaternary diffusion couple, Mg-0.64Al-0.04Sn-0.59Zn/Mg-0.79Al-2.42Sn-0.66Zn, annealed at 773 K for 250 h due to the present atomic mobilities (solid lines) and the experimental data (in symbols) by Bryan et al. [33]. The model-predicted composition-distance profiles from Zhong et al. [32] (dashed lines) are also superimposed in the figure for direct comparison. As can be seen in Figure 13, the model-predicted composition-distance profiles of Sn and Al in the present work show much better agreement with the experimental data of Bryan et al. [33], compared with the results from Zhong et al. [32]. The model-predicted composition-distance curve of Zn from both the present work and Zhong et al. [32] slightly deviate from the experimental data of Bryan et al. [33]. It should be noted that the difference in the Zn concentration in both end alloys was only 0.07 at.%, which may cause large difficulties in the accurate experimental measurement of Zn concentration.   [32] at 673, 723, 773, and 823 K compared with the experimental data [34,37]. Along the diagonal lines, the model-predicted values are exactly equal to the experimental ones. The dashed lines represent the interdiffusion coefficients multiplied with a pre-factor of 2 or 0.5.

Hcp Mg-Al-Zn-Sn Quaternary System
Based on the above comprehensive comparison among the model-predicted results from the present work, the ones by Zhong et al. [32], and the experimental data [34,37], the reliability of the atomic mobility descriptions of the hcp Mg-Al-Sn system was significantly improved by using the newly proposed strategy compared with the traditional approach. The major reason lies in that although 18 groups of diffusion couples were investigated by Zhou et al. [37] and Zhang et al. [34], only very scattered experimental interdiffusion coefficients at the intersection compositions of diffusion paths can be determined by the traditional methods and then utilized in the traditional optimization process, which may lead to the lower accuracy of the obtained atomic   [32] at 673, 723, 773, and 823 K compared with the experimental data [34,37]. Along the diagonal lines, the model-predicted values are exactly equal to the experimental ones. The dashed lines represent the interdiffusion coefficients multiplied with a pre-factor of 2 or 0.5.
Based on the above comprehensive comparison among the model-predicted results from the present work, the ones by Zhong et al. [32], and the experimental data [34,37], the reliability of the atomic mobility descriptions of the hcp Mg-Al-Sn system was significantly improved by using the newly proposed strategy compared with the traditional approach. The major reason lies in that although 18 groups of diffusion couples were investigated by Zhou et al. [37] and Zhang et al. [34], only very scattered experimental interdiffusion coefficients at the intersection compositions of diffusion paths can be determined by the traditional methods and then utilized in the traditional optimization process, which may lead to the lower accuracy of the obtained atomic  [32] at 673, 723, 773, and 823 K compared with the experimental data [34,37]. Along the diagonal lines, the model-predicted values are exactly equal to the experimental ones. The dashed lines represent the interdiffusion coefficients multiplied with a pre-factor of 2 or 0.5.
predicted composition-distance profiles of Sn and Al in the present work show much better agreement with the experimental data of Bryan et al. [33], compared with the results from Zhong et al. [32]. The model-predicted composition-distance curve of Zn from both the present work and Zhong et al. [32] slightly deviate from the experimental data of Bryan et al. [33]. It should be noted that the difference in the Zn concentration in both end alloys was only 0.07 at.%, which may cause large difficulties in the accurate experimental measurement of Zn concentration. Figure 13. Model-predicted composition-distance profiles of the only quaternary diffusion couple in quaternary system, Mg-0.64Al-0.04Sn-0.59Zn/Mg-0.79Al-2.42Sn-0.66Zn, annealed at 773 K for 250 h from the present atomic mobilities (solid lines) compared with these of Zhong et al. [32] (dashed lines) and the experimental data [33] (in symbols).
Based on the above analysis, a real improvement in the reproduction of the experimental data was achieved by the present work compared with the results of Zhong et al. [32], even though only one more quaternary diffusion couple was included in the present work. It is anticipated that the reliability of the atomic mobilities in the hcp Mg-Al-Zn-Sn quaternary system can be further improved by using the newly proposed strategy if more experimental composition profiles in the quaternary Mg-Al-Zn-Sn system are available. By contrast, the reliability of atomic mobilities in the hcp Mg-Al-Zn-Sn quaternary system cannot be improved based on the traditional method, no matter whether the experimental data for Mg-Al-Zn-Sn system are sufficient.
To illustrate the influence of Sn concentration and temperature on the inter0diffusivities of the hcp Mg-Al-Zn-Sn quaternary system, the matrix (α-Mg) phase with an average composition of 2.4 at.% Al and 0.56 at.% Zn in as-cast AZT640 (Mg-6Al-4Zn-0.6Sn, in wt.%), according to Dong et al. [45], was chosen as the target in the present work. According to the presently updated atomic mobility descriptions together with the Figure 13. Model-predicted composition-distance profiles of the only quaternary diffusion couple in quaternary system, Mg-0.64Al-0.04Sn-0.59Zn/Mg-0.79Al-2.42Sn-0.66Zn, annealed at 773 K for 250 h from the present atomic mobilities (solid lines) compared with these of Zhong et al. [32] (dashed lines) and the experimental data [33] (in symbols).
Based on the above analysis, a real improvement in the reproduction of the experimental data was achieved by the present work compared with the results of Zhong et al. [32], even though only one more quaternary diffusion couple was included in the present work. It is anticipated that the reliability of the atomic mobilities in the hcp Mg-Al-Zn-Sn quaternary system can be further improved by using the newly proposed strategy if more experimental composition profiles in the quaternary Mg-Al-Zn-Sn system are available. By contrast, the reliability of atomic mobilities in the hcp Mg-Al-Zn-Sn quaternary system cannot be improved based on the traditional method, no matter whether the experimental data for Mg-Al-Zn-Sn system are sufficient.
To illustrate the influence of Sn concentration and temperature on the inter0diffusivities of the hcp Mg-Al-Zn-Sn quaternary system, the matrix (α-Mg) phase with an average composition of 2.4 at.% Al and 0.56 at.% Zn in as-cast AZT640 (Mg-6Al-4Zn-0.6Sn, in wt.%), according to Dong et al. [45], was chosen as the target in the present work. According to the presently updated atomic mobility descriptions together with the thermodynamic descriptions [40], the interdiffusion coefficients of the Mg-Al-Zn-Sn quaternary system over a compositions range of 2.4 at.% Al, 0.56 at.% Zn, and 0-0.6 at.% Sn at 623, 673, and 723 K were predicted in Figure 14. As can be seen in Figure 14a

Conclusions
• A general and effective strategy for the maintenance of the CALPHAD atomic mobility database of multicomponent systems was developed based on the pragmatic numerical inverse method and HitDIC software; • Following the newly proposed strategy, the atomic mobility descriptions of the hcp Mg-Al-Zn and Mg-Al-Sn ternary systems were updated based on the experimental composition profiles in the respective ternary systems. It was found that the presently updated atomic mobilities of the hcp Mg-Al-Zn system provided a good fit for all of the experimental diffusion properties as did the previous assessment [32] using the traditional approach, while the presently updated atomic mobilities of the hcp Mg-Al-Sn system showed better agreement with the experimental diffusion properties than the previous assessment [32] using the traditional approach. Moreover, the variation trend of inter-diffusivities of the hcp Mg-Al-Zn and Mg-Al-Sn systems with the temperature and solute (i.e., Al, Zn, and Sn) concentrations was also fully analyzed; • Based on the updated atomic mobility descriptions of the hcp Mg-Al-Zn and Mg-Al-Sn systems, together with only one set of composition-distance profiles, the atomic mobility descriptions of the hcp Mg-Al-Zn-Sn quaternary system were further updated following the newly proposed strategy. A real improvement in the reproduction of experimental data was achieved by the present work compared with

Conclusions
• A general and effective strategy for the maintenance of the CALPHAD atomic mobility database of multicomponent systems was developed based on the pragmatic numerical inverse method and HitDIC software; • Following the newly proposed strategy, the atomic mobility descriptions of the hcp Mg-Al-Zn and Mg-Al-Sn ternary systems were updated based on the experimental composition profiles in the respective ternary systems. It was found that the presently updated atomic mobilities of the hcp Mg-Al-Zn system provided a good fit for all of the experimental diffusion properties as did the previous assessment [32] using the traditional approach, while the presently updated atomic mobilities of the hcp Mg-Al-Sn system showed better agreement with the experimental diffusion properties than the previous assessment [32] using the traditional approach. Moreover, the variation trend of inter-diffusivities of the hcp Mg-Al-Zn and Mg-Al-Sn systems with the temperature and solute (i.e., Al, Zn, and Sn) concentrations was also fully analyzed; • Based on the updated atomic mobility descriptions of the hcp Mg-Al-Zn and Mg-Al-Sn systems, together with only one set of composition-distance profiles, the atomic mobility descriptions of the hcp Mg-Al-Zn-Sn quaternary system were further updated following the newly proposed strategy. A real improvement in the reproduction of experimental data was achieved by the present work compared with the previous assessment. Furthermore, the influence of Sn concentration and temperature on the inter-diffusivities of the hcp Mg-Al-Zn-Sn quaternary alloys was also illustrated; • It is anticipated that the presently proposed strategy can serve as a standard for maintaining the CALPHAD atomic mobility database of different multicomponent systems.
Supplementary Materials: The following are available online at https://www.mdpi.com/article/ 10.3390/ma15010283/s1, Figure S1: Model-predicted composition-distance profiles of different hcp Mg-Al-Zn diffusion couples annealed at (a) 663 K for 144 h and (b) 708 K for 144 h as well as an enlarged composition-distance curve of Zn annealed at (c) 663 K for 144 h and (d) 708 K for 144 h from the present atomic mobilities (solid lines) compared with those of Zhong et al. [32] (dashed lines) and the experimental data [33] (symbols).